Question: $\int x^{-5}\,dx=$ $+C$
Answer: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{{-5}}\,dx&=\dfrac{x^{{-5}+1}}{{-5}+1}+C \\\\ &=-\dfrac14x^{-4}+C \end{aligned}$ In conclusion, $\int x^{-5}\,dx=-\dfrac14x^{-4}+C$